I have been playing Eve for about three years now on and off, and honestly it's not a game for the player who likes instant gratification when they play a game, Eve is deep and complex and can require a few months to really start to understand what the game is about as well as finding out what you like to do within the game universe, I'll try and give a description of the many occupations you can undertake in Eve.
1. Mining - Within the Eve universe there are asteroid belts which when harvested can yeild low to highend minerals that other players can buy to make the many ships and modules used to play the game. This can be very boring for some people and they will only do it if they need to get the proper minerals for the ships or modules that they want to build, other people will do this all the time so that they can either build stuff for themselves or build stuff to be sold to the other players in Eve.
2. Construction - This usually goes hand in hand with mining since you need the minerals to create the items you want to use or sell, players can purchase blueprints more commonly referred to as BPOs which they place into factory slots in either NPC or player owned stations along with the minerals required, after the required time passes the item will be ready for pick up and the blueprint as well as the item are available for the player to either sell or use for him or herself, this trade tends to be a little more expensive to get into especially when you approch building the large battleship and capital ships and as such tend to only be built by people in large corporations or alliances.
3. PVP/PVE - Player vs Player combat and player vs NPC ( more commonly known as ratting ) is another option for you as an eve player. A PVP player will make their money by either killing npc pirates in space and sell the salvaged loot to other players, or they will become pirates themselves who will wait in low security systems and kill players ships and steal the loot inside. Players can also run missions for any of the four factions in eve and gain loyalty points as well as money for completing the missions.
4. Trade - Another way to make your way in the Eve universe is by trading, certain skills will allow you to examine the markets in solar systems many light years away, this will allow you to see where some items may be sold at higher prices then another, you can then buy items in bulk where it is cheaper and sell them in the system where they go for higher prices
5 Corporate/alliance managment - Some people are just born leaders, as such these people can train to be the heads of major corporations and alliances the more skilled they become the larger they can make the corp or alliance they have.
Not every player does jsut one thing, many players either have other characters that they use for specific tasks, some do a little of everything on the one character, you can pretty much do anything that you want as long as it dosnt violate the EULA. If you are looking for a game with more depth and where you make your own story and your own history then Eve is for you, feel free to log on and send me a message I will be more then happy to help out new players get adjusted, my pilots name is Katarina Arisdeed.
Good luck and fly safe